scholarly journals The Reidemeister-Turaev torsion of standard Spin^c structures on Seifert fibered 3-manifolds

2012 ◽  
Vol 21 (4) ◽  
pp. 745-768
Author(s):  
Yuya Koda
Keyword(s):  
Turaev Torsion

scholarly journals SOME FINITENESS PROPERTIES FOR THE REIDEMEISTER–TURAEV TORSION OF THREE-MANIFOLDS

2010 ◽  
Vol 19 (03) ◽  
pp. 405-447 ◽  
Author(s):  
GWÉNAËL MASSUYEAU
Keyword(s):  
To Come ◽  
Finiteness Properties ◽  
Turaev Torsion

We prove for the Reidemeister–Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. In general, those properties require the manifolds to come equipped with an Euler structure and a homological parametrization.

scholarly journals LENS SPACE SURGERIES ALONG CERTAIN 2-COMPONENT LINKS RELATED WITH PARK’S RATIONAL BLOW DOWN, AND REIDEMEISTER-TURAEV TORSION

2013 ◽  
Vol 96 (1) ◽  
pp. 78-126 ◽  
Author(s):  
TERUHISA KADOKAMI ◽  
YUICHI YAMADA
Keyword(s):  
Main Tool ◽  
Lens Space ◽  
The Other ◽  
Dehn Surgery ◽  
Rational Homology ◽  
Blow Down ◽  
Alexander Polynomials ◽  
Other Hand ◽  
Turaev Torsion

AbstractWe study lens space surgeries along two different families of 2-component links, denoted by${A}_{m, n} $and${B}_{p, q} $, related with the rational homology$4$-ball used in J. Park’s (generalized) rational blow down. We determine which coefficient$r$of the knotted component of the link yields a lens space by Dehn surgery. The link${A}_{m, n} $yields a lens space only by the known surgery with$r= mn$and unexpectedly with$r= 7$for$(m, n)= (2, 3)$. On the other hand,${B}_{p, q} $yields a lens space by infinitely many$r$. Our main tool for the proof are the Reidemeister-Turaev torsions, that is, Reidemeister torsions with combinatorial Euler structures. Our results can be extended to the links whose Alexander polynomials are same as those of${A}_{m, n} $and${B}_{p, q} $.

scholarly journals Reidemeister–Turaev torsion modulo one of rational homology three-spheres

2003 ◽  
Vol 7 (2) ◽  
pp. 773-787 ◽  
Author(s):  
Florian Deloup ◽  
Gwenael Massuyeau
Keyword(s):  
Rational Homology ◽  
Turaev Torsion

scholarly journals SEIBERG–WITTEN INVARIANTS OF RATIONAL HOMOLOGY 3-SPHERES

2004 ◽  
Vol 06 (06) ◽  
pp. 833-866 ◽  
Author(s):  
LIVIU I. NICOLAESCU
Keyword(s):  
Homology Sphere ◽  
Rational Homology ◽  
Turaev Torsion ◽  
Rational Homology Sphere

We prove that the Seiberg–Witten invariants of a rational homology sphere are determined by the Casson–Walker invariant and the Reidemeister–Turaev torsion.

Seiberg-Witten Invariants of Lens Spaces

2001 ◽  
Vol 53 (4) ◽  
pp. 780-808 ◽  
Author(s):  
Liviu I. Nicolaescu
Keyword(s):  
Lens Space ◽  
Lens Spaces ◽  
Turaev Torsion

AbstractWe show that the Seiberg-Witten invariants of a lens space determine and are determined by its Casson-Walker invariant and its Reidemeister-Turaev torsion.

scholarly journals 3d-3d correspondence for mapping tori

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Sungbong Chun ◽  
Sergei Gukov ◽  
Sunghyuk Park ◽  
Nikita Sopenko
Keyword(s):  
Partition Function ◽  
Systematic Study ◽  
Geometric Structure ◽  
Gauge Theories ◽  
Complex Group ◽  
Mapping Tori ◽  
Non Linear ◽  
Turaev Torsion ◽  
Matter Fields

Abstract One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d $$ \mathcal{N} $$ N = 2 SCFT T [M3] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M3 and, secondly, is not limited to a particular supersymmetric partition function of T [M3]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d $$ \mathcal{N} $$ N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M3], and propose new tools to compute more recent q-series invariants $$ \hat{Z} $$ Z ̂ (M3) in the case of manifolds with b1> 0. Although we use genus-1 mapping tori as our “case study,” many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.

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